In nuclear reactors in which the primary coolant is essentially water, as for example in pressurised water reactors, the reactivity of the reactor core is controlled among other things by adding boron to the primary coolant. Boron is a neutron poison, which absorbs some of the neutron flux generated by the nuclear reactions in the reactor core. Thus when the boron concentration of the primary coolant increases, the heat released by the core of the reactor decreases. Conversely, when the boron concentration in the primary coolant decreases, the heat released by the reactor core increases.
The boron concentration in the primary coolant is adjusted automatically or manually in relation to set reactor control levels, for example in relation to the setting for the electrical power which the reactor has to provide to the high voltage electricity distribution grid.
With this object the reactor is provided with a circuit known as the REA. This circuit comprises means for injecting a solution comprising essentially water and not containing boron into the primary coolant with a view to downwardly adjusting the boron concentration in the primary coolant. The REA circuit also comprises means for injecting a concentrated solution containing 7000 ppm of boron into the primary coolant in order to adjust the boron concentration in the primary coolant upwards. In both cases the volume of primary coolant is maintained constant by removing from the primary circuit a volume of liquid corresponding to the volume injected.
It is thus very important for control of the nuclear reactor to know the boron concentration in the primary coolant at all times.
With this object the reactor is provided with one or more sensors (boron meters) designed to measure the boron concentration in the primary coolant.
The boron concentration of the primary coolant measured automatically by the boron meter is inaccurate (noise of the order of 7%) and is provided after a significant delay, of the order of some twenty minutes.
In order to overcome the measurement delay, the boron concentration in the primary coolant can be estimated by integrating the flows of water and concentrated solution injected into the primary coolant via the REA. These flows underlie changes in the boron concentration.
The flow integration method is based on the following equations.
The change dC in the boron concentration C of the primary coolant for a constant mass of primary coolant M is caused by injecting a charge of liquid having a boron concentration C*(concentrated boron or water solution) and by simultaneously removing a charge of primary coolant having concentration C. The mass balance is therefore written as:MdC=C*dm−Cdm where dm is the mass of both the charge of liquid injected and the charge of primary coolant withdrawn, where C*=0 ppm for a dilution and C*=7000 ppm for the injection of a concentrated boron solution.
If it is assumed that the injected and withdrawn flows are constant and the same, the balance becomes:MdC=(C*−C)qdt where q is the injected/withdrawn flow and dt is a time interval.
By integrating we obtain:
      ln    ⁡          (                        C          ⁡                      (            t            )                          -                  C          *                    )        =            ln      ⁡              (                              C            ⁡                          (              0              )                                -                      C            *                          )              -                  q        M            ⁢      t      where C(0) is the boron concentration in the primary coolant at t=0,that is
      C    ⁡          (      t      )        =            C      *        +                  (                              C            ⁡                          (              0              )                                -                      C            *                          )            ⁢              ⅇ                              -                          q              M                                ⁢          t                    or also
      (                  C        *            -              C        ⁡                  (          t          )                      )    =            (                        C          *                -                  C          ⁡                      (            0            )                              )        ⁢          ⅇ                        -                      q            Vol                          ⁢        t            if q is no longer a mass flow but a volume flow, Vol being the volume of primary coolant.
This process has the advantage that it allows the change in boron concentration after the end of the action of dilution or injection of concentrated boron solution (boron addition) to be quickly estimated. The fact that the delays associated with the time required for the charge to flow through the primary circuit and the time required for the injected charge to become diluted and for the boron concentration to become uniform in the primary coolant are not taken into account brings forward estimation of the boron concentration by some ten minutes.
The above equations can be used to simulate different types of action (dilution or boron addition) for a constant injection flow, and also to simulate a stationary situation (no injection). They provide the final concentration (after the action) on the basis of an initial concentration (before the action). It is therefore necessary to update the starting concentration C(0) before each action, and this enables an iterative approach to be used.
In this iterative approach, the following equation is applied to each time step k:
      (                  C        *            -              C                  k          +          1                      )    =            (                        C          *                -                  C          k                    )        ⁢          ⅇ                        -                      q            Vol                          ⁢        Δ        ⁢                                  ⁢        t            where Ck is the estimated boron concentration in the primary coolant in step k, C* being chosen to be 0 or 7000 ppm, as before, depending on whether the action in progress is dilution or boron addition. Δt is the duration of a time step.
The first disadvantage of the process of integrating flows is that there is long term drift in the estimated value in relation to the actual value (see for example FIG. 2). This drift arises from cumulated errors in each time step, due for example to the difference between the flow q used by the equations and the actual injected flow.
The second disadvantage arises from the initialisation stage, which is required for an iterative process of this kind. Initialisation must be as accurate as possible, otherwise the results will be skewed at each time step. It can be done by selecting a mean of the measurements made by the boron meter over a given time as an initial value C0 for the boron concentration in the primary coolant. In the case of FIGS. 2 and 4 to 6 the iterative process (line 2) has been initialised using the mean of the values found during the four hours preceding the start of the process. In this case it is however impossible to be sure that the mean obtained represents the actual boron concentration at the moment when the iterative process started. Initialisation may also be carried out by using the boron concentration measured by chemical determination as the initial value, which is accurate, but tedious and not very fast.
In any event, the cumulative effect of these two disadvantages results in this method being not very robust.
Furthermore, the process using the integration of flows ignores other sources of variation in boron concentration, such as for example the injection of fluid into the primary circuit from the pressuriser, the RCV tank, the demineralisation filters, etc.